Viscosity effect on free surface waves in fluids

Abstract

The frequencies and damping coefficients of gravitational-capillary waves are found for a wide range of controlling dimensionless parameters. The transition to the limiting cases of deep water and an ideal fluid is analyzed. In the parameter plane, the boundary between the regions of oscillatory and aperiodic perturbations is determined and the region of weak damping is indicated. The equilibrium state of thin liquid films with account for the Van der Waals forces is considered and the dispersion equation for the capillary-Van der Waals surface waves is obtained. For a suitably chosen frequency scale, this equation is the same as that for gravitational-capillary waves. The physical conditions making it possible to observe capillary and Van der Waals waves in thin fluid layers are estimated.